Page:Dictionary of Greek and Roman Biography and Mythology (1870) - Volume 3.djvu/585

Rh PTOLEMAEUS. mentioned the versions of the genuine work which are found with those of the Almagest. 5, 6. De Analemrnate and Planispfiaerium. These works are obtained from the Arabic. Fa- bricius, who had not seen them, conjectures that they are the same, which is not correct. The Analemma is a collection of graphical processes for facilitating the construction of sun-dials, grounded on what we now call the orthographic projection of the sphere, a perspective in which, mathematically speaking, the eye is at an infinite distance. The Plaimphere is a description of the stereographic projection, in which the eye is at the pole of the circle on which the sphere is pro- jected. Delambre seems to think, from the former work, that Ptolemy knew the gnomonic projection, in which the eye is at the centre of the sphere : but, though he uses some propositions which are closely connected with the theory of that projec- tion, we cannot find any thing which indicates dis- tinct knowledge of it. There is but one edition of the work De Analemrnate, edited by Commandine, Home, 1562, 4to. (Lalande says there is a Vene- tian title of the same date. He also mentions another edition, Rome, 1572, 4to., perhaps an error of copying). Nothing is told about the Arabic original, or the translator. The Planisphaerium first appeared in print in the edition of the Geo- graph}^ Rome (?), 1507, fol. (Hoffmann) ; next in Valder's collection, entitled " Sphaerae atque As- tro rum Coelestium Ratio, . . .," Basle (? no place is named), 1536, 4to. With this is joined the Pla- nisphaerium of Jordanus. There is also an edition of Toulouse, 1544, fol. (Hoffmann), But the best edition is that of Commandine, Venice, 1558, 4to. Lalande says it was reprinted in 1588. Suidas records that Ptolemy wrote airXucris iTri(f>aueias aipas, which is commonly taken to be the work on the planisphere. Both the works are addressed to Syrus. 7. nepl vTToBiaecov rau TrXauccixevwi/, De Planefa- rum Hypotliesibus. This is a brief statement of the principal hypotheses employed in the Almagest (to which it refers in a preliminary address to Syrus) for the explanation of the heavenly motions. Simplicius refers to two books of hypotheses, of which we may suppose this is one. It was first printed (Gr. Lat.) by Bainbridge, with the Sphere of Proclus and the canon above noted, London, 1620, 4to., with a page of Bainbridge's corrections at the end; afterwards by Halma, as already de- scribed. 8. 'ApfioviKwv ^L§Kla y'. This treatise on the theory of the musical scale was first published (Gr. Lat.) in the collection of Greek musicians, by Gogavinus. Venice, 1562, 4to. (Fabricius). Next by Wallis (Gr. Lat.), Oxford, 1682, 4to., with various readings and copious notes. This last edition was reprinted (with Porphyry's com- mentary, then first published) in the third volume of Wallis's works, Oxford, 1699, folio. 9. Uepl KpiTTiplov Kot riy^ixoviKov, De Jttdicandi Facultate et Animi Frincipatu^ a metaphysical work, attributed to Ptolemy. It was edited by Bouillaud (Gr. Lat.), Paris, 1663, 4to., and the edition had a new title page (and nothing more) in 1681. In Lalande we find attributed to Ptolemy, " Re- gulae Artis Mathematicae" (Gr. Lat.), — 1569, 8vo., with explanations by Erasmus Rein hold. The collection made by Fabricius of the lost PTOLEMAEUS. S73 works of Ptolemy is as follows : — From Simplicius, ITepi H€Tp7}(r€ws ixov6§i€os, to prove that there can be only three dimensions of space ; TIfpl poirwv fii€iov, mentioned also by Eutocius ; 2Tozx«a, two books of hypotheses. From Suidas, three books Mi^xaviKwu. From Heliodorus and Simplicius, 'OirTiK-n trpayfiaTeia. From Tzetzes, Tlepn^ynais ; and from Stephen of Byzantium, Uep'nrAovs. There have been many modem forgeries in Ptolemy's name, mostly astrological. It must rest an unsettled question whether the work written by Ptolemy on optics be lost or not. The matter now stands thus : Alhazen, the principal Arab writer on optics, does not mention Ptolemy, nor indeed, any one else. Some passages from Roger Bacon, taken to be opinions passed on a manu- script purporting to be that of Ptolemy, led Mon- tucla to speak highly of Ptolemy as an optical writer. This mention probably led Laplace to ex- amine a Latin version from the Arabic, existing in the Royal Library at Paris, and purporting to be Ptolemy's treatise. The consequence was Laplace's assertion that Ptolemy had given a detailed account of the phenomenon of astronomical refraction. This remark of Laplace led Humboldt to examine the manuscript, and to call the attention of Delambre to it. Delambre accordingly gave a full account of the work in his Histoire de I Adronomie Ancienne, vol. ii. pp. 411 — 431. The manuscript is headed Incipit Liber Ptholemaei de Optiois sive Aspectihus translatus ah Ammiraco [or Ammirato'] Eugenio Siculo. It consists of five books, of which the first is lost and the others somewhat defaced. It is said there is in the Bodleian a manuscript with the Avhole of five books of a similar title. The first three books left give such a theory of vision as might be expected from a writer who had the work attributed to Euclid in his mind. But the fifth book does actuall}'^ give an account of refraction, with ex- perimental tables upon glass, water, and air, and an account of the reason and quantity of astronomical refraction, in all respects better than those of Al- hazen and Tycho Brah^, or of any one before Cas- sini. With regard to the genuineness of the book, on the one hand there is its Avorthiness of Ptolemy on the point of refraction, and the attribution of it to him. On the other hand, there is the absence of allusion, either to the Almagest in the book on optics, or to the subject of refraction in the Alma- gest. Delambre, who appears convinced of the ge- nuineness, supposes that it was written after the Al- magest. But on this supposition, it must be supposed that Ptolemy, who does not unfrequently refer to the Almagest in his other writings, has omitted to do so in this one, and that upon points which are taken from the Almagest, as the assertion that the moon has a colour of its own, seen in eclipses. But what weighs most with us is the account which Delambre gives of the geometry of the author. Ptolemy was in geometry, perspicuous, elegant, profound, and powerful ; the author of the optics could not even succeed in being clear on the very points in which Euclid (or another, if it be not Euclid) had been clear before him. Delambre ob- serves, in two passages, '^ La demonstration de Ptole'me'e est fort embrouillde ; celle d'Euclide est et plus courte et plus claire,".... " Euclide avail prouve' proposition 21 et 22, que les objets pa- raissent diminue's dans les miroirs convexes. On entrevoit que Ptole'mee a voulu aussi de'montrer lea Kieraes propositions." Again, the refraction apait,